Multi-layer coded modulation for non-ergodic block fading channels

ABSTRACT

A multi-layer coded modulation technique is disclosed for a wireless communication system with non-ergodic channels, which is particularly advantageous for multiple-input multiple-output (MIMO) systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and is a nonprovisional of U.S.Provisional Application No. 60/710,095, entitled “DESIGN OF MULTI-LAYERCODED MODULATION FOR NON-ERGODIC BLOCK FADING CHANNELS,” filed on Aug.22, 2005, the contents of which are incorporated herein by reference.

BACKGROUND OF INVENTION

The invention relates generally to modulation techniques in wirelesscommunication systems.

Multiple-input multiple-output (MIMO) data transmission throughsparsely-spaced antennas at both the transmitter and receiver provides asubstantial increase in spectral efficiency of wireless links. MIMOtransmission can potentially accomplish a multiplexing gain (i.e., aninformation rate increase due to virtual multiple wireless links) and adiversity gain (i.e., a spatial diversity due to multiple antennas inaddition to time-domain and frequency-domain diversity). A key torealizing high data rates in such MIMO systems is a practical codedmodulation scheme. From a data block size perspective, one maycategorize prior art coded modulation schemes as follows. For smallblock size (e.g., smaller than ten), there are many solutions, such asorthogonal space-time block codes, linear dispersion codes, threadedalgebraic space-time codes, and lattice space-time codes. When the blocksize is around several hundred, options include space-time trellis codesand “wrapped” space-time codes.

Consider, however, moderate-to-large block sizes (e.g., larger than athousand) which are suitable for most data traffic in broadbandcommunications. In this design regime, existing schemes are mostly basedon powerful binary random codes (e.g., turbo codes or LDPC codes). Theyinclude bit-interleaved coded modulation (BICM), (see E. Zehavi, “8-PSKTrellis Codes for a Rayleigh Channel,” IEEE Trans. Communi., Vol. 40,pp. 873-84 (May 1992); Y. Liu et al., “Full Rate Space-Time TurboCodes,” IEEE J. Select. Areas in Commun., Vol. 19, pp. 969-80 (2001)),multilevel coded modulation (MLC) (see H. Imai and S. Hirakawa, “A NewMultilevel Coding Method using Error-Correcting Codes,” IEEE Trans.Inform. Theory, Vol. 23, pp. 371-77 (May 1977); L. J. Lampe et al.,“Multilevel Coding for Multiple Antenna Transmission,” IEEE Trans.Wireless Commun., Vol. 3, pp. 203-08 (2004)), and stratified diagonalBLAST (see M. Sellathurai and G. Foschini, “Stratified Diagonal LayeredSpace-Time Architectures: Signal Processing and Information TheoreticAspects,” IEEE Trans. Sig. Proc., Vol. 51, pp. 2943-54 (November 2003)).The recently proposed stratified D-BLAST is a coded D-BLAST, wheredifferent coding rates and transmission powers are assigned to differentthreads of D-BLAST. Among these schemes, BICM is considered to be simpleand asymptotically capacity-approaching in both ergodic and non-ergodicchannels, with the computation of a number of turbo receiver iterations.MLC requires channel-specific design of coding rates and constellationmapping functions for the different levels of MLC. On the other hand,MLC can be optimized for various objectives, such as providing unequalerror protection. With the simple multi-stage decoding receiver, MLC isasymptotically capacity-approaching in ergodic MIMO fadingchannels—however is not so in non-ergodic fading channels.

SUMMARY OF INVENTION

A multi-layer coded modulation technique is disclosed for a wirelesscommunication system with non-ergodic channels, which is particularlyadvantageous for multiple-input multiple-output (MIMO) systems. At thetransmitter, multiple information data blocks are independently coded bydifferent binary random encoders and mapped to complex symbols. Thesymbols from all the layers are transmitted in distinct transmissionslots (e.g., space-time slots or space-frequency slots). At thereceiver, a successive decoding structure is employed to recover theinformation data layer-by-layer. A systematic design procedure isdisclosed which maximizes the information rate subject to an upper boundon the decoding error probability. This can be achieved by providingequal error protection of different layers at the target decoding errorprobability. Spatial interleaving is advantageously employed, whichoffers superior and consistent performance in various channelenvironments. With proper design of the multi-layer coded modulationarrangement, good performance can be obtained in non-ergodic channels.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates a transmitter and receiver structure arranged toimplement multi-layered coded modulation in accordance with anembodiment of an aspect of the invention.

FIG. 2 is a flowchart of a design procedure for the multi-layered codedmodulation arrangement.

FIG. 3 illustrates examples of different spatial interleaver designs.

DETAILED DESCRIPTION

FIG. 1 illustrates a multiple-input multiple-output (MIMO) systemsuitable for practice of an embodiment of the present invention.

As depicted in FIG. 1, the transmitter receives multiple data blocks fortransmission. The information to be transmitted can either come in theform of multiple data blocks (e.g., progressive layered media data) orcan be divided into multiple data blocks with appropriate lengths. Themultiple data blocks are independently coded by binary random encoders111, 112, . . . 115 with proper coding rates and preferably mapped tocomplex symbols at 121, 122, . . . 125. As depicted at 131, 132, . . .135, each layer can be multiplied by a complex factor α_(i) for bothpower control and phase rotation (herein, for discussion purposes, letα_(i)=1, ∀i). The symbols from all the layers are then mapped todistinct transmission slots (e.g., space-time or space-frequency slots)in the order that is determined by spatial interleaver 140, as furtherdescribed herein. The symbols are then transmitted from multipleantennas 141, 142, . . . 145 in K symbol intervals (or K OFDMsubcarriers).

The following baseband discrete-time MIMO signal model can be used todescribe the transmission: $\begin{matrix}{{y_{k} = {{\sqrt{\frac{\gamma}{N_{t}}}H_{k}\Pi_{k}x_{k}} + n_{k}}},} & {{k = 1},2,\cdots\quad,K,}\end{matrix}$where γ denotes the average transmission power from all transmitantennas (or equivalently the SNR); N_(t) (N_(r)) denotes the number oftransmit (receive) antennas; y_(k)∈C^(N) ^(r) , ∀k is the receivedsignal vector; H_(k) is the N_(r)×N_(t) complex MIMO channel matrix atthe k-th instance of general MIMO fading channels; Π_(k) is apermutation matrix for spatial interleaving whose construction isfurther discussed below; x_(k)∈Ω^(N) ^(t) , ∀k, is the transmitted datasymbol vector taking values from the M -ary QAM or M-ary PSKconstellation Ω; n_(k)˜N_(c)(0,I) is a noise vector. The above signalmodel can be rewritten as $\begin{matrix}\begin{matrix}{{y_{k} = {{\sqrt{\frac{\gamma}{N_{t}}}{\sum\limits_{i = 1}^{M}{h_{k,{\pi_{k}{\lbrack i\rbrack}}}x_{k,i}}}} + n_{k}}},} & {{k = 1},2,\cdots\quad,K,}\end{matrix} & (1)\end{matrix}$where h_(k,π) _(k) _([i]) denotes the N_(r)×N_(t) ^(i) spatialsub-channel matrix of the ith layer of the multi-layer coded modulationscheme which transmits from N_(t) ^(i)(N_(t) ^(i)≧1) transmit antennas,with Σ_(i=1) ^(M) N_(t) ^(i)≡N_(t); π_(k) [i] denotes the N_(t)^(i)-size index set of sub-transmit antenna channel(s) used by the i-thlayer transmission, which is one-to-one determined by Π_(k) and can bebetter understood through examples depicted in FIG. 3 and described infurther detail herein; x_(k,i) is the N_(t) ^(i)-size signal vectortransmitted by the i-th layer at the k-th instance.

As one example, the channel model can be used to represent narrow-bandMIMO channels such that data {x_(k)} are transmitted in time domain andchannels {H_(k)} in general are time-correlated due to Doppler fading as$\begin{matrix}{\left\{ H_{k} \right\}_{i,j} \simeq {\sum\limits_{n = {- {\lceil{\hat{f}}_{d}\rceil}}}^{\lceil{\hat{f}}_{d}\rceil}{{\beta_{i,j}\lbrack n\rbrack}\quad{\mathbb{e}}^{j\quad 2\quad\pi\quad{{nk}/K}}}}} & (2)\end{matrix}$where {H_(k)}_(i,j) denotes the (i,j)-th element of matrix H_(k);{circumflex over (f)}_(d)

f_(d)KT, with f_(d) being the maximum Doppler frequency and T being theduration of one symbol interval; β_(i,k)[n], ∀n are independentlycircularly symmetric complex Gaussian random variables, with variancesdetermined by the Doppler spectrum and normalized as Σ_(n)Var{β_(i,j)[n]}=1; it is assumed that for different (i,j)-antenna pairs,β_(i,j) are mutually independent. As another example, the channel modelcan be used to represent wide-band MIMO OFDM channels such that data{x_(k)} are transmitted in frequency domain and channels {H_(k)} ingeneral are frequency-correlated due to multipath fading as$\begin{matrix}{\left\{ H_{k} \right\}_{i,j} = {\sum\limits_{n = 0}^{L - 1}{{\alpha_{i,j}\lbrack n\rbrack}\quad{\mathbb{e}}^{{- j}\quad 2\quad\pi\quad{{nk}/K}}}}} & (3)\end{matrix}$where α_(i,j)[n], ∀n are independent circularly symmetric complexGaussian random variables, with variances determined by the delay spreadprofile of the L-tap multipath fading channels and normalized as Σ_(n)Var{α_(i,j)[n]}=1; it is assumed that α_(i,j) are mutually independentfor different (i,j)-antenna pairs.

As depicted in FIG. 1, a successive decoding structure can be employedat the receiver to recover the information data layer-by-layer, giventhe channel matrices H_(k), ∀k and the SNR γ. The transmitted signalsare received by antennas 151, 152, . . . 155 and a spatial deinterleaver150 is applied. The decoding then proceeds sequentially from layer-1(the first decoded layer) to layer-M (the last decoded layer). Thereceiver performs a linear MMSE demodulation by treating both un-decodedlayers' signals and ambient noise as background noise, e.g., the i-thlayer symbol vector is demodulated as $\begin{matrix}{{\hat{x}}_{k,i} = {\sqrt{\frac{\gamma}{N_{t}}}{{h_{k,{\pi_{k}{\lbrack i\rbrack}}}^{H}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}{\sum\limits_{j > i}^{M}{h_{k,{\pi_{k}{\lbrack j\rbrack}}}h_{k,{\pi_{k}{\lbrack j\rbrack}}}^{H}}}}} \right)}^{- 1} \cdot {\overset{\sim}{y}}_{k,i}}}} & (4) \\{\quad{= {{C_{k,i} \cdot \sqrt{\frac{\gamma}{N_{t}}}}{{h_{k,{\pi_{k}{\lbrack i\rbrack}}}^{H}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}{\sum\limits_{j \geq i}^{M}{h_{k,{\pi_{k}{\lbrack j\rbrack}}}h_{k,{\pi_{k}{\lbrack j\rbrack}}}^{H}}}}} \right)}^{- 1} \cdot {\overset{\sim}{y}}_{k,i}}}}} & (5) \\{with} & \quad \\{{C_{k,i} = {I_{N_{r}^{i}} + {\frac{\gamma}{N_{t}}{h_{k,{\pi_{k}{\lbrack i\rbrack}}}^{h}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}{\sum\limits_{j > i}^{M}{h_{k,{\pi_{k}{\lbrack j\rbrack}}}h_{k,{\pi_{k}{\lbrack j\rbrack}}}^{H}}}}} \right)}^{- 1}h_{k,{\pi_{k}{\lbrack i\rbrack}}}}}},} & \quad\end{matrix}$where I_(N) denotes the identity matrix of size N; y _(k,i) denotes thereceived signals with already decoded layers' signals subtracted. TheLMMSE-I above denotes the traditional LMMSE filter that minimizes themean-square error between x_(k,i) and {circumflex over (x)}_(k,i). TheLMMSE-II above denotes the LMMSE filter specifically adapted hereinwhich, compared to LMMSE-I, does not include the term h_(k,π) _(k)_([i])h_(kπ) _(k) _([i]) ^(H) inside the inverted matrix. Moreover, itcan be shown that when N_(t) ^(i)=1, LMMSE-I and LMMSE-II only differ bya positive multiplier (i.e., C_(k,i) degen the samesignal-to-interference-plus-noise-ratio (SINR) of the LMMSE output{circumflex over (x)}_(k,i). Alternatively, {circumflex over (x)}_(k,i)can be written as $\begin{matrix}\begin{matrix}{{\hat{x}}_{k,i} = {w_{k,i}^{H}\quad{\overset{\sim}{y}}_{k,i}}} \\{= {{\underset{\underset{{{equiv}.\quad{channel}}\quad{gain}}{︸}}{w_{k,i}^{H}\sqrt{\frac{\gamma}{N_{t}}}h_{k,{\pi_{k}{\lbrack i\rbrack}}}}x_{k,i}} + {\underset{\underset{{equiv}.\quad{noise}}{︸}}{w_{k,i}^{H}\left( {{\sqrt{\frac{\gamma}{N_{t}}}{\sum\limits_{j > i}^{M}{h_{k,{\pi_{k}{\lbrack j\rbrack}}}x_{k,j}}}} + n_{k}} \right)}.}}}\end{matrix} & (6)\end{matrix}$With the knowledge of the distribution of the equivalent noise, the softinformation (the likelihood ratio) of x_(k,i) can be computed fromequation 6. Based on the soft information of x_(k), the channel decoderperforms decoding for layer-k. Next, layer-k's signals are reconstructedfrom the hard decoding output if decoding is successful (or from thesoft decoding output if decoding has failed), and subtracted from thereceived signal to obtain {tilde over (y)}_(k,i+1).

Note that a successful decoding is claimed only if all layers arecorrectly decoded; therefore, the receiver may opt to terminate thedecoding process to save complexity where an error in any layer causesan overall decoding failure. This strategy is particularly justified inprogressive layered media transmission such that the recovery of theenhancement layers (if transmitted by higher layers of the disclosedscheme) alone is useless without the correct recovery of the base layers(if transmitted by lower layers). A standard way of testing theintegrity (and correctness) of the decoded data includes using a cyclicredundancy check, which implies a negligible loss of data rate.

It can be shown that the structure depicted in FIG. 1, when used inergodic fading channels, is capable of achieving optimal performancewhen all M layers transmit with equal power and with coding ratescomputed as follows. For an M-layer system, $\begin{matrix}{{{\sum\limits_{i = 1}^{M}{\log\quad{\det\left\lbrack {I_{N_{t}^{i}} + {\frac{\gamma}{N_{t}}{h_{i}^{H}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}{\sum\limits_{j > i}^{M}{h_{j}h_{j}^{H}}}}} \right)}^{- 1}h_{i}}} \right\rbrack}}} = {\log\quad{\det\left\lbrack {I_{N_{r}} + {\frac{\gamma}{N_{t}}H\quad H^{H}}} \right\rbrack}}},} & (7)\end{matrix}$See M. K. Varanasi and T. Guess, “Optimum Decision Feedback MultiuserEqualization with Successive Decoding Achieves the Total Capacity of theGaussian multiple-access channel,” in Asilomar Conference on Signals,Systems & Computers (November 1997). By enumerating H=H_(k), k=1, . . ., K above and taking expectation with respect to H

{H_(k)}_(k=l) ^(K), $\begin{matrix}{{{\sum\limits_{i = 1}^{M}{E_{H}\underset{\underset{C_{i}{({\gamma,H})}}{︸}}{\left\{ {\frac{1}{K}{\sum\limits_{i = 1}^{M}{\log\quad{\det\left\lbrack {I_{N_{t}^{i}} + {\frac{\gamma}{N_{t}}h_{i}^{H}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}\quad{\sum\limits_{j > i}^{M}{h_{j}\quad h_{j}^{H}}}}} \right)^{- 1}h_{i}}} \right\rbrack}}}} \right\}}}} = {E_{H}\underset{\underset{C{({\gamma,H})}}{︸}}{\left\{ {\frac{1}{K}{\sum\limits_{k = 1}^{K}{\log\quad{\det\left\lbrack {I_{N_{r}} + {\frac{\gamma}{N_{t}}H_{k}\quad H_{k}^{H}}} \right\rbrack}}}} \right\}}}},} & (8)\end{matrix}$where E_(H){f(H)} denotes the expectation of f(H) over H;E_(H)C_(i)(γ,H) is the average mutual information of the i-th layer ofsuccessive decoding; and and E_(H)C(γ,H) is the ergodic capacity of thisblock fading MIMO channel. Note the following:

-   -   The equality in equation 8 indicates that the disclosed        modulation scheme is capable of achieving the capacity of        ergodic MIMO fading channels under the assumption that Gaussian        signaling is employed with coding rate r_(i)=E_(H)C_(i)(γ,H) and        successive LMMSE-based cancellation and decoding is performed at        each layer. In particular, the equality holds true only when all        M layers transmit with equal power, i.e., α_(i)=1, ∀i.    -   The ergodic-capacity-achieving property always holds, regardless        of the specific values of (N_(r), N_(t), N_(t) ^(i), ∀i). At the        receiver side, the successive decoding at the i-th layer is        concerned with an equivalent N_(t) ^(i)-input N_(r)-output        vector channel (if N_(t) ^(i)>1). Hence, there exists a possible        tradeoff between the decoding complexity reduction (M instead of        N_(t) decoders, M<N_(t)) and the demodulation complexity        increase (demodulator for vector-input instead of for        scalar-input).    -   The ergodic-capacity-achieving property of the modulation scheme        hinges on the fact that each layer experiences ergodic fading        channels with infinite diversity order. In particular, there is        no loss of optimality if each layer transmits only from fixed        transmit antenna(s) and thus without explicitly exploiting        transmit-antenna diversity.    -   In practice, the ergodic MIMO fading channel capacity can be        approached (by a fraction of dB) by coded modulation schemes        based on binary random codes (e.g., turbo codes or LDPC codes)        with very large block size and by successive LMMSE cancellation        and decoding (as discussed above). Note that the coded        modulation design motivated by the equation above does not        follow the conventional design path started from pairwise error        probability (PEP) of the decoder, but, nonetheless, leads to        pragmatically good performance in MIMO systems.

In non-ergodic fading channels, due to the limited observations ofchannel states in one data block, the outage capacity is commonly usedas a measure of performance limit. For instance, the outage probabilityto support rate r_(i) transmission of the i-th layer is defined asP_(out) ^(i)(γ,r_(i))=Pr(C_(i)(γ,H)<r_(i))=E_(H){1_({C) _(i) _((γ,H)<r)_(i}) }, γ∈R⁺, r_(i)∈R⁺. Intuitively, in order to maximize the totalinformation rate, it is desirable to provide equal error protection forall layers at all SNRs γ∈R⁺, i.e., P_(out) ^(i)(γ, r_(i))=P_(out)^(j)(γ, r_(j)), ∀i≠j, ∀γ. This objective is readily achieved in ergodicfading channels. The design, however, is generally more involved innon-ergodic channels, since the function P_(out) ^(i)(γ, r_(i)) ischaracterized by the statistics of H, in addition to the SNR γ and thedesign rate r_(i). The notion of achieving equal error protection at allSNRs γ∈R⁺ is valid only if P_(out) ^(i)(γ, r_(i)), ∀i have the sameshape and differ only by shift, which is in general not true innon-ergodic fading channels.

Since it is generally infeasible to achieve equal error protection forlayers at all SNRs, it is advantageous to relax the design problem suchthat each layer's outage probability is upper bounded by the same targeterror rate. The optimization problem can be stated as $\begin{matrix}{{\max\quad{\sum\limits_{i = 1}^{M}r_{i}}}{{{s.t.\quad{P_{out}^{i}\left( {\gamma,r_{i}} \right)}} \leq {\hat{P}}_{e}},{\forall i},{r_{i} > 0},{\forall{i.}}}} & (9)\end{matrix}$It can be then shown that the optimal solutions to the aboveoptimization problem, when existing for given γ, are {r_(i)*}_(i=1) ^(M)satisfyingP _(out) ¹(γ,r ₁*)≡P _(out) ²(γ,r ₂*)≡ . . . ≡P _(out) ^(M)(γ, r_(M)*)≡{circumflex over (P)} _(e)   (10)where the superscript * denotes the optimal value of individualvariables. Note that the parameters that are explicitly optimized aboveare the information rates r_(i) of all layers (achieved jointly bybinary coding and MPSK or MQAM constellation; it is possible to haver_(i)≧1); in fact, the optimal solutions also implicitly depend onspace-time (or space-frequency) channel interleaving functions, asdiscussed below. It should be further remarked that the solution to theabove equation only achieves the equal error protection at a particularSNR (such as to satisfy the given target error rate {circumflex over(P)}_(e)), instead of all SNRs.

It should also be noted that it is possible to also jointly optimizeα_(i). Nevertheless, it is advantageous to avoid it because in practicevarying α_(i) will result in larger peak-to-average-power ratio (PAPR)at each transmit antenna due to the use of spatial interleaver; and thejoint optimization of r_(i) and α_(i) is also numerically demanding.

Note that equation 10 can be solved by solving M sub-problems, asP_(out) ^(i)(γ, r_(i)*)≡{circumflex over (P)}_(e), i=1, . . . , M.Because an LMMSE demodulator of a particular layer always treats theother undecoded layers signals as interference, and the information rater_(i) only affects the decoding performance but not the LMMSEdemodulation performance. Assume each layer only transmits from onetransmit antenna (i.e., N_(t) ^(i)=1, ∀i), then it can be shown from thesignal model above that the instantaneous SINR ξ at the output of thei-th layer LMMSE demodulator is given by $\begin{matrix}{\xi_{k,i} = {\frac{\gamma}{N_{t}}{h_{k,{\pi_{k}{\lbrack i\rbrack}}}^{H}\left( {I_{N_{r}} + {\frac{\gamma}{N_{t}}{\sum\limits_{j > i}^{M}{h_{k,{\pi_{k}{\lbrack j\rbrack}}}h_{k,{\pi_{k}{\lbrack j\rbrack}}}^{H}}}}} \right)}^{- 1}h_{k,{\pi_{k}{\lbrack i\rbrack}}}}} & (11)\end{matrix}$Using a Gaussian approximation of the output of the LMMSE filter, theinstantaneous mutual information of the i-th layer in equation 8 can bere-written as $\begin{matrix}{{C_{i}\left( {\gamma,\mathcal{H}} \right)} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\underset{\underset{r_{ideal}{(\xi_{k,i})}}{︸}}{\log\left( {1 + \xi_{k,i}} \right)}}}} & (12)\end{matrix}$In practice, given the same (γ, H), the information rate supported bypractical coded modulation is always strictly less thanr_(ideal)(ξ_(k,i)).

As a heuristic approach, one can replace each term of r_(ideal)(ξ_(k,i))by the actual rate function of practical coded modulation schemes, e.g.,r_(ldpc)(ξ) of LDPC codes. To be more specific, the function r_(ldpc)(ξ)can be defined as the information rate provided by LDPC codes at the SNRof ξ and the FER of {circumflex over (P)}_(e),r _(ldpc)(ξ)={r _(ldPC) ∈R ⁺ |P _(FER)(ξ, r _(ldpc))={circumflex over(P)} _(e) , ξ∈R ⁺}  (13)Note that the FER performance is well represented by the outageprobability of the fading channel when the block size is large. Thefunction r_(ldpc)(ξ) can be increased by properly optimizing the LDPCcode design and construction in AWGN channels which leads to betterperformance in MIMO fading channels. A rate function of practical codedmodulation, e.g., r_(ldpc)(ξ) of the ensembles of practical LDPC codes,can be generated as follows: (1) construct LDPC codes with a given codeblock length and with various coding rates (e.g., {circumflex over(r)}=0.1k, k=1, . . . , 9) from LDPC code ensembles; (2) run Monte Carlosimulations of the LDPC decoding in discrete-input-continuous-outputAWGN channels, where LDPC code bits are modulated into discreteconstellation with Gray mapping; (3) read the minimum SNR {circumflexover (ξ)} required to achieve a target FER (e.g., 5e-3) from theFER-vs-SNR plots for various rates; (4) by polynomial interpolation ofall pairs of {circumflex over (r)} and {circumflex over (ξ)},r_(ldpc)(ξ) can be obtained.

Although spatial interleaving is unnecessary to achieve capacity inergodic MIMO fading channels, spatial interleaving plays a moreimportant role in non-ergodic MIMO fading channels. Consider threepossible candidates for a spatial interleaving function: (I) no spatialinterleaving; (II) random (uniform) spatial interleaving; and (III)spatial ordering (assisted with a low-rate feedback channel). Thedisadvantages of a type-I design in non-ergodic channels is evident—thetransmit-antenna diversity is not exploited for individual layers. Thetype-II design uniformly exploits the transmit antenna diversity foreach layer. This goal can be achieved by the known D-BLAST structure asdepicted in FIG. 3B. Alternatively, a random design can be utilizedwhich is illustrated by FIG. 3A. More specifically, at the k-thinstance, k=1, . . . , K, a uniform permutation set Â of the natural setA={1, 2, . . . , N_(t)} is independently generated. Let${{\pi_{k}\lbrack i\rbrack} = \left\{ \hat{\mathcal{A}} \right\}_{n_{1}}^{n_{2}}},{with}$$n_{1} = {1 + {\sum\limits_{j = 1}^{i - 1}N_{t}^{j}}}$ and$n_{2} = {\sum\limits_{j = 1}^{i}{N_{t}^{j}.}}$It can be shown that any realization of a type-II spatial interleavershares the property that${\frac{1}{K}{\sum\limits_{k = 1}^{K}{1_{j \in {\pi_{k}{\lbrack i\rbrack}}}\overset{K->\infty}{\longrightarrow}\frac{1}{N_{t}}}}},{\forall j},$meaning that the i-th layer employs each transmit antenna evenly.Illustrative examples of a type-II random spatial interleaver design andthe D-BLAST design are shown in FIG. 3. The type-III design is describedas follows. The basic idea of a type-III design is to rank spatialsub-channels' quality, and based on that ranking to transmit a differentlayer from the appropriate transmit antenna. First, the Frobenius normof each spatial sub-channel ${q_{i}\overset{\Delta}{=}{h_{i}}_{F}},$which is adopted to indicate the sub-spatial channel quality, iscomputed at the receiver. Second, by ranking all q_(i)'s at thereceiver, the resultant index set {S_(i)}_(i=1) ^(M)={S_(i)∈Z⁺,1≦S_(i)≦M|q_(s) ₁ ≧q_(s) ₂ ≧ . . . ≧q_(s) _(M) } is sent back to thetransmitter, through a low-rate feedback channel. Third, the transmitterthen transmits layer-i from the S_(i)-th transmitter antenna ∀i, withthe information rate r_(i). For simplicity, we drop the sub-script k andassume N_(t) ^(i)=1, ∀i. Note that for a type-III design, in order toreduce the implementation cost, the rates {r_(i)} are preferablydetermined off-line (by following a procedure similar to the onedescribed below) based on the ensemble of the equivalently rankedchannels {h_(S) _(i) }, rather than the instantaneous channelrealizations. Loosely speaking, the type-II design reflects the idea of(passive) equal-gain transmission, while the type-III design practicesthe (proactive) selective transmission. Numerical experiments show thatboth type-II and type-III yield better performance than a type-I designin non-ergodic fading channels. Type-II provides relatively moreconsistent and superior performance in various channel profiles; atype-III design could be useful in support of higher information ratefor layer-1 transmission (the layer first decoded and faced with thestrongest interference).

FIG. 2 is a flowchart illustrating the optimization of the modulationdesign for non-ergodic fading channels, in accordance with an embodimentof an aspect of the invention. First, initialization is performed. At210, γ and {circumflex over (P)}_(e) are set, as well as the statisticalprofiles (delay profile, Doppler spectrum) of the non-ergodic MIMOfading channels. The spatial interleaver$\left\{ \prod\limits_{k} \right\}_{k = 1}^{K}$is also set. Then, Monte Carlo sampling is performed at steps 221 to225. S samples are generated where S is a sufficiently large number soas to sample the non-ergodic channel matrices H_(k). At step 222,generate${\mathcal{H}\overset{\Delta}{=}\left\{ H_{k} \right\}_{k = 1}^{K}},$for example, by using equations 2 or 3. At step 223, compute the SINRξ_(k,i), ∀k, i using equation 11 above. Then, at step 224, compute theinstantaneous mutual information C_(i,s)(γ, H) using equations 12 and13. Finally, after computing the above for each sample, at step 225, anempirical probability distribution function is formed of{C_(i)(γ, ℋ)}_(i = 1)^(M)from the Monte Carlo samples. Then, at steps 231 and 232, the optimalsolution is obtained. For each of the M layers, the coding rate r_(i)*is found such that P_(out) ^(i)(γ, r_(i)*)≡{circumflex over (P)}_(e) .This can be accomplished by line search. It can be shown that for scalarflat-fading channels at-fading channels the optimized design obtained bythe above is capacity-achieving, universal (independent of thestatistics of the channel coefficients), and of equal error protectionat all SNR's. For general non-ergodic fading channels, however, thedesign is not capacity-achieving, is not universal, and only achievesequal error protection at a single SNR.

It is useful to compare the disclosed modulation scheme with existingcoded modulation schemes. Although the present modulation scheme has asuperficial structural similarity to multilevel coded modulation (MLC),the design outputs of MLC are coding rates and constellation partitionof different levels, where the design outputs of the present approachare coding rates and transmission powers of different layers. See, e.g.,U. Wachsmann et al., “Multilevel Codes: Theoretical Concepts andPractical Design Rules,” IEEE Trans. Inform. Theory, Vol. 45, pp.1361-91 (July 1999). The design of both schemes in non-ergodic fadingchannels are usually dependent on the channels' statistical profiles.Both schemes can asymptotically achieve the capacity of ergodic fadingchannels and approach the capacity of non-ergodic fading channels,however by different routes. MLC computes multi-stage decoding whereindividual level's decoding is conditioned on the decoding results ofearlier-decoded levels, and the mutual information of each MLC level'sequivalent channel is noise-limited, e.g., for a three-level 8-ASK MLCscheme, each level's mutual information goes to one (the maximum valuefor binary-input signaling of each MLC level) as SNR goes to infinity.On the contrary, the present invention utilizes successive cancellationdecoding where an individual layer's decoding is independent of thedecoding results of earlier-decoded layers (assuming that the decodedlayers' signals are ideally cancelled out), and the mutual informationof each layer's equivalent channel is interference-limited, e.g., for atwo-layer example above, the SINR of the layer-1's equivalent channelconverges to the signal-to-interference (SIR) |α₁|²/|α₂|² as SNR γ goesto infinity.

Bit-interleaved coded modulation (BICM) is so far the most widely-usedcoded modulation scheme in the large block size regime, because of itssimple and robust design and capacity-approaching performance. It isworth noting that in single-antenna systems, turbo signal processing(i.e., the iteration between demodulator and decoder) is not needed anda conventional non-iterative receiver is enough to achieve optimumperformance as long as Gray mapping is used. See G. Caire et al.,“Bit-Interleaved Coded Modulation,” IEEE Trans. Inform. Theory, Vol. 44,pp. 927-46 (May 1998). On the other hand, in MIMO systems, turboiterative processing is crucial to successively cancel out the spatialinterference, even when an optimal APP demodulator is used. Note thatthe present invention can also be used to carry out iterativesuccessive-decoding, for better receiver performance in non-ergodicfading channels and for finite-length codes. In practice, however, theextra processing delay introduced in turbo signal processing is notalways affordable, and it is accordingly advantageous herein to focus onlow-processing-delay receiver designs. The non-iterative BICM-LMMSE(i.e., BICM employing a LMMSE demodulator) and the above-disclosedreceivers have roughly the same computational complexity and processingdelay in transmitting the same total information rate and using the samemodulation constellation, based on the observation that the complexityand the delay of both demodulation and decoding are approximately linearin block size. Furthermore, if the block size effect on decodingperformance is ignored, the non-iterative BICM-LMMSE demodulatorperformance is the same as the layer-1 demodulation performance in thepresent scheme, but the layer-1 performance after decoding is betterthan that of BICM-LMMSE. This is because the optimized scheme describedabove employs for its layer-1 stronger error-correction coding than thatfor BICM-LMMSE, assuming both schemes have the same total informationrate and the same constellation. Indeed, based on simulations, theoptimized modulation scheme herein disclosed can even outperform anon-iterative BICM-APP receiver. From simulation examples in realisticMIMO fading channels, the present invention with practical codedmodulation (QPSK, block size 4096) can perform only 2.5 dB from theoutage capacity in support of 3.0 bits/Hz/s rate transmission. For codedMIMO systems, as the overall diversity order goes to infinity (orpractically very large), it is observed that the relative performancegain by applying an optimal APP demodulator diminishes compared to theuse of a linear MMSE demodulator.

While exemplary drawings and specific embodiments of the presentinvention have been described and illustrated, it is to be understoodthat that the scope of the present invention is not to be limited to theparticular embodiments discussed. Thus, the embodiments shall beregarded as illustrative rather than restrictive, and it should beunderstood that variations may be made in those embodiments by workersskilled in the arts without departing from the scope of the presentinvention as set forth in the claims that follow and their structuraland functional equivalents.

1. A method of modulation in a wireless communication system, comprising: receiving at least a first and second data block, encoding independently the first and the second data blocks in separate layers and mapping encoded data blocks into first and second symbols, applying a spatial interleaver to the first and second symbols before transmission, so that a receiver applying successive cancellation decoding can recover layer-by-layer at least the first data block from the transmission.
 2. The method of claim 1 wherein each layer is transmitted at an information rate that is optimized such that each layer's outage probability is upper bounded by a target error rate.
 3. The method of claim 2 wherein the optimized information rates for each layer are determined by forming an empirical probability distribution function of mutual information at each layer from Monte Carlo samples.
 4. The method of claim 1 wherein the spatial interleaver arranges the symbols in accordance with a uniform permutation set.
 5. The method of claim 1 wherein the spatial interleaver arranges the symbols in accordance with rankings of spatial sub-channels quality as provided through a feedback channel.
 6. The method of claim 1 wherein the transmission utilizes two or more transmit antennas.
 7. The method of claim 1 wherein the transmission occurs across a non-ergodic channel.
 8. A transmitter for a wireless communication system, comprising: a plurality of encoders and modulators arranged in layers so as to independently encode at least a first a second data block in separate layers and map encoded data blocks into first and second symbols, and a spatial interleaver adapted to receive the first and second symbols and rearrange the first and second symbols before transmission, the transmission arranged so as to allow a receiver applying successive cancellation decoding to recover layer-by-layer at least the first data block from the transmission.
 9. The transmitter of claim 8 wherein each layer is transmitted at an information rate that is optimized such that each layer's outage probability is upper bounded by a target error rate.
 10. The transmitter of claim 9 wherein the optimized information rates for each layer are determined by forming an empirical probability distribution function of mutual information at each layer from Monte Carlo samples.
 11. The transmitter of claim 8 wherein the spatial interleaver arranges the symbols in accordance with a uniform permutation set.
 12. The transmitter of claim 8 wherein the spatial interleaver arranges the symbols in accordance with rankings of spatial sub-channels quality as provided through a feedback channel.
 13. The transmitter of claim 1 further comprising two or more transmit antennas.
 14. The transmitter of claim 1 wherein the transmission occurs across a non-ergodic channel.
 15. A receiver for a wireless communication system, comprising: a spatial deinterleaver adapted to receive a transmitted signal and output a deinterleaved signal, and a plurality of demodulators and decoders coupled to the spatial deinterleaver, the plurality of demodulators and decoders arranged in layers so as to recover a first data block in a first layer from the deinterleaved signal and cancel the recovered first data block from the deinterleaved signal before recovering a next data block in a next layer.
 16. The receiver of claim 15 wherein each layer in the transmitted signal has an information rate that is optimized such that each layer's outage probability is upper bounded by a target error rate.
 17. The receiver of claim 16 wherein the optimized information rates for each layer are determined by forming an empirical probability distribution function of mutual information at each layer from Monte Carlo samples.
 18. The receiver of claim 15 wherein the spatial deinterleaver rearranges symbols in the transmitted signal in accordance with a uniform permutation set.
 19. The receiver of claim 15 further comprising two or more receive antennas.
 20. The receiver of claim 15 wherein the transmission occurs across a non-ergodic channel. 